where

t =

duration in seconds

S=

conductor section, expressed in sqmm

I =

effective short-circuit current in amperes,

K =

115

for copper conductors with PVC insulation

143

for copper conductors insulated with ethylene propylene rubber and polypropylene

74

for aluminium conductors with PVC insulation

87

for aluminium conductors insulated with ethylene propylene rubber and polypropylene

115

corresponding to a temperature of 160°C, for soft-soldered joints between copper conductors.

The above formula assumes that the heating of the conductors, during the passage of the short-circuit current, is adiabatic.

The formula is better represented in the following way:

where (I²t) ) is the integral Joule for the duration of the short circuit (in A²s), "A" is equal to the current and "s" to the time.

For short-circuit lasting more than a few times, you can get the value of (I²t) assuming "I" the true RMS in amperes of the short- circuit current and "t" the duration, in seconds, of the same short-circuit.

For short durations (<0.1 s), when the asymmetry of the short-circuit current is relevant and for protective limiting devices of pass-through energy, the value (I²t) must be specified by the manufacturer of the protective device. The formula should be checked for a short circuit that occurs at any point of the protected conductors. The values of the constant "K" were determined on the basis of the values of the maximum temperatures allowed during ordinary service and during short circuit for the isolation of wires.

These parameters, in this analysis referred to conductors with PVC insulation, operating at an operating temperature of 70°C and at a short circuit temperature of 160°C, will be recalculated according to the temperature class required (temperature class must be provided by customer at the time of size request) and considering that the maximum temperature reached by the conductors must not exceed the maximum surface temperature for the design specific class temperature.

Therefore, according to what described above, a correct dimensioning of the electrical conductors is of primary importance, in order to avoid the occurrence of systematic critical temperatures that may be the cause of ignition of explosion just because of exceeding the safety threshold determined by the class temperature, by which the enclosure will have to be installed and operate in continuous service.

Considering that these enclosures must be suitable for installation in explosion proof areas (‘Ex d’ with directly entry or ‘Ex de’ with indirect entry), hence subject to certification by qualified internationally recognized body, therefore the dimensioning must be responsive to all the parameters set by the reference standards, such as:IEC 60079-0 o EN 60079-0 o CEI EN 60079-0: Explosive atmospheres – Part 0: Equipment – General requirements.IEC 60079-1 o EN 60079-1 o CEI EN 60079-1: Explosive atmospheres – Part 1: Equipment protection by flameproof enclosures “d”.IEC 60079-7 o EN 60079-7 o CEI EN 60079-7: Explosive atmospheres - Part 7: Equipment protection by increate safety “e”.IEC 60079-14 o EN 60079-14 o CEI EN 60079-14: Explosive atmospheres Part 14: Electrical installations design, selection and erection.

With equal importance, but for the use of the equipment intended to be included within and / or above the lid of the enclosures, must also be considered the specific electrical regulations such as:IEC 60439-1 o EN 60439-1 o CEI EN 60439-1: Low-voltage switch gear and control gear assemblies - Part 1: General requirements. (currently in force until the end of 2014, after this date will be replaced with the new IEC 61439-1 or EN 61439-1 or IEC 61439-1).IEC 60439-3 o EN 60439-3 o CEI EN 60439-3: Low-voltage switch gear and control gear assemblies – Part 3: Distribution boards (currently in force until the end of 2014, after this date will be replaced with the new IEC 61439- or EN 61439-3 or IEC 61439-3).Should be considered, of course, all applicable specific reference rules for equipment that will be included in the enclosures with the function of "switch gear or control gear assemblies", such as circuit breakers, terminal blocks, etc…

The basic parameters to be considered for this dimensioning are:

• The current-limiting of thermo-magnetic circuit breaker;
• The acceptable thermal stress of conductors and/or cables.

The current-limiting of thermo-magnetic circuit breaker, is usually defined by limitation curves that can be summarized as follows:

Graphic 1

• Short Circuit presumed current (kA rms)
• Limited pass-through specific energy (A²s)

Graphic 1 shows, for an ease interpretation, the characteristic curves of thermo-magnetic circuit breakers of Acti9 series Schneider Electric, specifically, the circuit breakers iC60N series.

As can be seen, the straight line indicated in red represents the energy "A²s" of a short-circuit current of a half period (10 ms), which indicates the energy that would be dissipated in the absence of limitation of the protection device.

We can proceed now with the sizing of conductors that will be used to support the current demands, assuming the input data that the customer must notify us at the time of size request.

So, for this dimensional hypothesis, we will assume that the client has provided us with the following input data:

• Ambient temperature: 45°C
• Temperature Class: T5
• Breaking capacity: 10 kA at 400VAC
• Total installed and working power: 20 kW at 400VAC
• Rated current for incoming line three pole plus neutral: 32A at 400VAC
• Rated power for each outgoing lighting feeders: 2 kW at 230VAC
• Rated current for each outgoing lighting feeders  one phase plus neutral: ~ 9A at 230VAC (n° 10 outgoing feeders)
• Rated voltage: 400/230VAC ± 10%
• Rated frequency: 50 Hz ± 5%
• Electric system: TN-S, three phase plus neutral
• Protection system: PE, separate from neutral
• Tripping curve: C (standard loads)
• Degree of mechanical protection: IP66
• Coefficient of contemporaneity: 1 (all outgoing feeders operate in parallel and at nominal load of 2 kW, for a total of 20 kW)

Based on these input data, we proceed to the first stage of sizing, selecting the circuit breakers suitable for the application, that is:

• Main incoming circuit breaker, three pole plus neutral, suitable for a total load of 20 kW at 400 VAC, with characteristic curve “C” for standard loads.

Where:I = rated current, in AmpereP = total power, in kW (20 kW)V = rated voltage, in kV (0,4kV)Cosphì = assumed value 0,9you will then have that I= 20/(1,73 . 0,4kV . 0,9) = 32A.

• Two pole distribution circuit breakers, suitable for a unit load each of 2kW at 230VAC, with characteristic curve “C” for standard loads

According to the derating temperature table (see catalog Acti9 Schneider Electric) and in accordance with CEI EN 60898-1 standard, for a circuit breaker of 400VAC, responsive to the specifications required by the customer, we will adopt the type iC60N that has a breaking capacity (Icu) of 10kA at 400VAC.

On the basis of this first dimensioning, we’ll proceed to its temperature derating, up to find the electrical quantity responsive to our needs, (the rated current of this range of circuit breakers is referred to 30° C).

• 32A at 30°C, downgraded to 45°C, gives 30.2 A which downgraded by a further 20% for installation in an ambient with prevented ventilation, gives 24.16 A, and then not responding to our needs.
• 40A at 30°C, downgraded to 45°C, gives 37,74A which downgraded by a further 20% for installation in an ambient with prevented ventilation, gives 30,19A, and then not responding to our needs.
• 50A at 30°C, downgraded to 45°C, gives 46,93A which downgraded by a further 20% for for installation in an ambient with prevented ventilation, gives 37,54A, and then responding to our needs.

It should be noted that the ambient temperature, it’s not the one inside the enclosure, but rather the outside, so the above mentioned derating is the result of the experience of our tests laboratory in Villesse. Given the complexity of these inspections, for convenience of calculation, we assume in this analysis that further downgrade is equal to 20% (in reality it is an internal parameter variable depending on the layout of the equipment and then determined only by our tests laboratory).

So, according to the above, we will select a circuit breaker of 50A at 30°C, but working at 45°C with a corresponding current of ~ 38 A, redundant with respect to the nominal current request.Obviously this means that, according to this downgrade, will be installed a 50A nominal main incoming circuit breaker with four pole but with maximum capacity of 38A, utilized at the intended temperature inside the enclosure.Let's take an indicative example of the size criteria, assuming to define what will be the limited energy by a circuit breaker of this series, with a rated current of 50A for a short-circuit current of 10kA rms.

Graphic 2

As can be seen from the Graphic 2, the short-circuit current of 10kA rms may dissipate up to 1000000A (K²s), but using a 50A switch, type iC60N, as evidenced by the characteristic curve in the graphic, the thermal stress would significantly reduce, leading to 60000A (A²s). Reducing it up to 16 times lower, will be a considerable advantage in terms of overheating of conductors.

Considering now that it has already carried out the verification of the "Filiation" upstream/ downstream (technique of filiation which will be the subject of another discussion), we can  proceed to the sizing of the outgoing lighting circuit breakers at 230VAC:

• 10 outgoing feeders for light circuits, with two pole circuit breakers of 2 kW each - 6 kA, iC60a model suitable for a unit load of 2 kW at 230VAC, with characteristic "C" for standard loads. These circuit breakers, according to the filiation technique, although having a breaking capacity of 6 kA at 230 VAC, will be coordinated by a reinforced Icu of 10kA and, then, adapted to the customer's request (please refer to the section "Filiation" on the Guide at low-voltage System of Schneider Electric).

On the basis of this first dimensioning, we can proceed to its temperature derating, up to find the electrical quantity responsive to our needs. The rated current of this range of circuit breakers is referred to 30° C.

• 10 A at 30°C, downgraded to 45°C, gives 9,4 A which downgraded by a further 20% for installation in an ambient with prevented ventilation, gives 7,52 A, and then not responding to our needs.
• 16 A at 30°C, downgraded to 45°C, gives 15,09 A which downgraded by a further 20% for installation in an ambient with prevented ventilation, gives 12,07 A, and then responding to our needs.

So, according to the above, we will select a circuit breaker of 16A at 30°C, but working at 45°C with a corresponding current of ~ 13 A.

Obviously this means that, according to this downgrade, will be installed 16A nominal main incoming circuit breakers with four pole but with maximum capacity of 13A, utilized at the intended temperature inside the enclosure.

Similarly, we make an indicative example of the size criterion, assuming that we want to define what will be the energy limited by a circuit breaker of this series, with a rated current of 16A for a short-circuit current of 10kA rms.

Graphic 3

As can be seen in the Graphic 3, referring to 2 pole main circuit breakers - 16A, iC60a series, with breaking capacity of 6kA, (with filiation 10kA), the value of the specific energy is 24500A²s , for a time of 10 ms. Conductors must be sized to withstand this specific energy, without distortion and without generating overheating not conform to temperature class requested by the customer.

We can now speak about the dimensioning of the electrical conductors to be installed within the "Panel Board". Comparing the current capacity of conductors and/or cables according to IEC 60332-1 or IEC 60332-3C Standards, designed for an ambient temperature in free air of 30°C, for single core copper conductors with PVC insulation and voltage Uo/U of 0.45/0.75 kV, type H07Z1-K (extract from Prismian Group catalog for cables and accessories 2013 edition), we have:

So, on the basis of these values, we will do a further alignment according to the temperature, the laying side by side (conductors under load, with coefficient of contemporaneity 1) and according to the correction factor for installation in an ambient with prevented ventilation:

• for laying side by side of 10 systems under load on two levels =  K 0,73
• for ambient temperature (inside of the panel) of 45°C = K 0,71
• coefficient of installation in ambient with prevented ventilation = K 0,8

bringing the sum of these downgrades to the total value of Kt = ~ 0,415

Assumed a nominal current of 38 A, for the incoming conductors and the distribution system (an alternative to the distribution system with conductors is the bus-bar system), the optimal section results to be of 25 sqmm, with current capacity of 89 A at 30°C, but downgraded with the value of Kt 0,415, brings its value to 36.94 A, lower than the nominal value of 38A. We will select the sections immediately above of 35 sqmm, with a range of current of 110A at 30°C, which will give a flow of current, always with the same derating, of 45,65A, suitable for section and also for pass-through energy which is the result of to the formula “ I²t ≤ K²S²”.In which for the "K" value we assume 115, referring to copper conductors with PVC insulation, and "S" will be the section of the conductors selected of 35 sqmm.So, I²t (60000 A²s) must be less than K²S² (115² x 35² = 16200625) and, as it turns, the  I²t value is below the value of 60000 A²s.

We proceed similarly to the verification of the downstream conductor cross section of the 2kW two pole circuit breakers:

• for laying side by side of 10 systems under load on two levels =  K 0,73
• for ambient temperature (inside of the enclosure) of 45°C = K 0,71
• coefficient of installation in an ambient with prevented ventilation = K 0,8

bringing the sum of these downgrades to the total value of Kt = ~ 0,415.

Assumed a nominal current of 13A, the optimal section results of 1.5 sqmm, with current capacity of 15.5A at 30°C, but downgraded with the value of Kt 0,415, brings the value to 6.43A, not able to meet the subtended load. Other suitable size will be selected such as that of 6 sqmm, with nominal current of 36A at 30°C, which will give a flow of current of 14.94A, always with the same derating, suitable for the section and also for the pass-through energy that is responsive to the formula “I2t ≤ K2S2”.In which the value of "K" assumes 115, referring to copper conductors with PVC insulation and "S" will be the section of the conductors selected 6 sqmm.

So, I²t (24500 A²s) must be less than K²S² (115² x 6² = 476100 ) and, as it turns, the I²t value is below the value of 24500 A²s.

We conclude this second part saying that all activities of electro-mechanical sizing are the prerogative of the manufacturer of the Panel Boards in explosion-proof execution: analysis, calculations and the resulting executive project are of its responsibility, putting the plate certifying the compliance with the relevant Standards.